Chaos Reborn client uses one TCP connection to the server's port 80. It doesn't use UDP so no need to configure your router to play. It doesn't open ports on the client's machine so there's no need for enabling ports on your personal firewall or configure port forwarding.

However antivirus and firewall software can disable the outgoing connection so you need to make sure that ChaosRebornWin32.exe / ChaosRebornWin64.exe is not blacklisted in them.

Some ISPs and routers are filtering the HTTP traffic that goes through them (and some of them are just injecting stuff in the HTTP responses) so the Chaos Server also listens for connections on port 8001. If you have connection problems you can try using this port. To do this when your connection fails on the login screen you should hold down the SHIFT key on your keyboard and while holding it you should click the "CONNECT TO SERVER" button. The "Connecting..." label will change to "Alt Connecting" and your client will start using the alternative port.